Abstract
We continue the analysis of the geometry of generic Minkowski \( \mathcal{N} \) = 1, D = 4 flux compactifications in M-theory using exceptional generalised geometry, including the calculation of the infinitesimal moduli spaces. The backgrounds can be classified into two classes: type-0 and type-3. For type-0, we review how the moduli arise from standard de Rham cohomology classes. We also argue that, under reasonable assumptions, there are no appropriate sources to support compact flux backgrounds for this class and so the only solutions are in fact G2 geometries. For type-3 backgrounds, given a suitable \( {\partial}^{\prime }{\overline{\partial}}^{\prime } \)-lemma, we show that the moduli can be calculated from a cohomology based on an involutive sub-bundle of the complexified tangent space. Using a simple spectral sequence we prove quite generally that the presence of flux can only reduce the number of moduli compared with the fluxless case. We then use the formalism to calculate the moduli of heterotic M-theory and show they match those of the dual Hull-Strominger system as expected.
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Acknowledgments
We thank Mariana Graña, Rahim Leung and especially David Tennyson for helpful discussions. GRS is supported by an EPSRC DTP studentship. DW is supported in part by the STFC Consolidated Grant ST/T000791/1 and the EPSRC New Horizons Grant EP/V049089/1. We acknowledge the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (Project ID 39083149) and the University of California Irvine for hospitality and support during part of this work.
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Smith, G.R., Waldram, D. M-theory moduli from exceptional complex structures. J. High Energ. Phys. 2023, 22 (2023). https://doi.org/10.1007/JHEP08(2023)022
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DOI: https://doi.org/10.1007/JHEP08(2023)022